When will the number of neurons in AI systems equal the human brain?
Some back of the envelope calculations :


  number of neurons in AI systems 


The number of neurons in AI systems is a little tricky to calculate, Neural Networks and Deep Learning are 2 current AI systems as you call them, specifics are hard to come by (If someone has them please share), but data on parameters do exist, parameters are more analogous to synapses (connections) than neurons (the nodes in between connections) somewhere in the range of 100-160 billion is the current upper number for specialized networks.

Deriving the number of neurons in AI systems from this number is a stretch since these AIs emulate certain types of connections and sub assemblies of neurons, but let's continue...


  equal those of the human brain?


So now let's look at the brain, and again this are all contested numbers. Number of neurons ~ 86 Billion, Number of Synapses ~ 150 Trillion, another generalization: average number of synapses per neuron ~ 1,744.

So now we have something to compare, and I can't stress this enough, these are all wonky numbers, so let's make our life a little easier and divide :

Number of Synapses (Brain ) : 150 trillion /  Number of parameters AIs : 150 billion = 1,000 or in other words current AIs would have to scale by a factor of one thousand their connections to be on par with the brain...

Number of Neurons (Brain ) : 86 Billion / Number of Neurons AIs ( 150 billion / 1,744 )  = 86 Million equivalent AI Neurons

Which makes sense, mathematically at least : you can multiply the factor ( 1000 ) times the current number of equivalent AI Neurons ( 86 million) to get the number of neurons in the human brain (86 Billion)


  When ?


Well,let's use  moore's law ( number of transistors processing power doubles about every 2 years ) as a rough measure of technological progress: 

     #AI NEURONS            YEAR
     86,000,000             2016
     172,000,000            2018
     344,000,000            2020
     688,000,000            2022
     1,376,000,000          2024
     2,752,000,000          2026
     5,504,000,000          2028
     11,008,000,000         2030
     22,016,000,000         2032
     44,032,000,000         2034
     88,064,000,000         2036


     # NEURONS HUMAN BRAIN 
     86,000,000,000


So, if all this made sense to you, somewhere around the year 2035.